Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Persistent bundles over a two dimensional compact set

"Vegeu el resum a l'inici del document del fitxer adjunt."

Non-covalent and covalent protein labeling in two-dimensional gel electrophoresis.

Over the past decades, several sensitive post-electrophoretic stains have been developed for an identification of proteins in general, or for a specific detection of post-translational modifications such as phosphorylation, glycosylation or oxidation. Yet, for a visualization and quantification of protein differences, the differential two-dimensional gel electrophoresis, termed DIGE, has become the method of choice for a detection of differences in two sets of proteomes. The goal of this review is to evaluate the use of the most common non-covalent and covalent staining techniques in 2D electrophoresis gels, in order to obtain maximal information per electrophoresis gel and for an identification of potential biomarkers. We will also discuss the use of detergents during covalent labeling, the identification of oxidative modifications and review influence of detergents on finger prints analysis and MS/MS identification in relation to 2D electrophoresis.

Sample preparation for two-dimensional gel electrophoresis.

The choice of sample preparation protocol is a critical influential factor for isoelectric focusing which in turn affects the two-dimensional gel result in terms of quality and protein species distribution. The optimal protocol varies depending on the nature of the sample for analysis and the properties of the constituent protein species (hydrophobicity, tendency to form aggregates, copy number) intended for resolution. This review explains the standard sample buffer constituents and illustrates a series of protocols for processing diverse samples for two-dimensional gel electrophoresis, including hydrophobic membrane proteins. Current methods for concentrating lower abundance proteins, by removal of high abundance proteins, are also outlined. Finally, since protein staining is becoming increasingly incorporated into the sample preparation procedure, we describe the principles and applications of current (and future) pre-electrophoretic labelling methods.

Establishing two-dimensional gels for the analysis of Leishmania proteomes.

Several different sample preparation methods for two-dimensional electrophoresis (2-DE) analysis of Leishmania parasites were compared. From this work, we were able to identify a solubilization method using Nonidet P-40 as detergent, which was simple to follow, and which produced 2-DE gels of high resolution and reproducibility.

Mapping the proteome of Leishmania Viannia parasites using two-dimensional polyacrylamide gel electrophoresis and associated technologies.

In this study we have demonstrated the potential of two-dimensional electrophoresis (2DE)-based technologies as tools for characterization of the Leishmania proteome (the expressed protein complement of the genome). Standardized neutral range (pH 5-7) proteome maps of Leishmania (Viannia) guyanensis and Leishmania (Viannia) panamensis promastigotes were reproducibly generated by 2DE of soluble parasite extracts, which were prepared using lysis buffer containing urea and nonidet P-40 detergent. The Coomassie blue and silver nitrate staining systems both yielded good resolution and representation of protein spots, enabling the detection of approximately 800 and 1,500 distinct proteins, respectively. Several reference protein spots common to the proteomes of all parasite species/strains studied were isolated and identified by peptide mass spectrometry (LC-ES-MS/MS), and bioinformatics approaches as members of the heat shock protein family, ribosomal protein S12, kinetoplast membrane protein 11 and a hypothetical Leishmania-specific 13 kDa protein of unknown function. Immunoblotting of Leishmania protein maps using a monoclonal antibody resulted in the specific detection of the 81.4 kDa and 77.5 kDa subunits of paraflagellar rod proteins 1 and 2, respectively. Moreover, differences in protein expression profiles between distinct parasite clones were reproducibly detected through comparative proteome analyses of paired maps using image analysis software. These data illustrate the resolving power of 2DE-based proteome analysis. The production and basic characterization of good quality Leishmania proteome maps provides an essential first step towards comparative protein expression studies aimed at identifying the molecular determinants of parasite drug resistance and virulence, as well as discovering new drug and vaccine targets.

Fronts from two-dimensional dispersal kernels: Beyond the nonoverlapping-generations model

Most integrodifference models of biological invasions are based on the nonoverlapping-generations approximation. However, the effect of multiple reproduction events overlapping generations on the front speed can be very important especially for species with a long life spam . Only in one-dimensional space has this approximation been relaxed previously, although almost all biological invasions take place in two dimensions. Here we present a model that takes into account the overlapping generations effect or, more generally, the stage structure of the population , and we analyze the main differences with the corresponding nonoverlappinggenerations results

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Effective one-dimensional square well for two-dimensional quantum wires

The symmetrical two-dimensional quantum wire with two straight leads joined to an arbitrarily shaped interior cavity is studied with emphasis on the single-mode approximation. It is found that for both transmission and bound-state problems the solution is equivalent to that for an energy-dependent one-dimensional square well. Quantum wires with a circular bend, and with single and double right-angle bends, are examined as examples. We also indicate a possible way to detect bound states in a double bend based on the experimental setup of Wu et al.

Two-dimensional clusters of liquid 4He

The binding energies of two-dimensional clusters (puddles) of¿4He are calculated in the framework of the diffusion Monte Carlo method. The results are well fitted by a mass formula in powers of x=N-1/2, where N is the number of particles. The analysis of the mass formula allows for the extraction of the line tension, which turns out to be 0.121 K/Å. Sizes and density profiles of the puddles are also reported.